Crowdsourcing Contests with Private Types and Evaluation Uncertainty

Abstract

We introduce a general model of crowdsourcing contests in which the performance of an agent is driven by his privately known ability type (adverse selection), his costly effort choice and it is further affected by evaluation uncertainty or luck (moral hazard). We show that when the marginal cost of effort is sufficiently large and the solvers' types, as well as, the evaluation uncertainty are independent and identically distributed respectively, there exists a unique Bayes Nash equilibrium effort. This equilibrium effort is in symmetric and pure strategies and involves inactive types. Our model includes as special cases the Tullock contest (Tullock, 1980), the all-pay auction model with private information of Moldovanu et al. (2001), and the symmetric effort with evaluation uncertainty model of Lazear et al. (1981) that have been studied separately thus far. Our results suggest that several comparative statics results of the all-pay auctions with private information are robust in the presence of noisy feedback.

Keywords: crowdsourcing, contests, existence, uniqueness, pure-strategy Bayes-Nash equilibrium, private information, moral hazard